Simplified Design for Concurrent Statistical Zero-Knowledge Arguments

This paper shows that the protocol presented by Goyal et al.can be further simplified for a one-way function,with the simplified protocol being more practical for the decisional Diffie-Hellman assumption.Goyal et al.provided a general transformation from any honest verifier statistical zero-knowledge argument to a concurrent statistical zero-knowledge argument.Their transformation relies only on the existence of one-way functions.For the simplified transformation,the witness indistinguishable proof of knowledge protocols in"parallel"not only plays the role of preamble but also removes some computational zero-knowledge proofs, which Goyal et al.used to prove the existence of the valid openings to the commitments.Therefore,although some computational zero-knowledge proofs are replaced with a weaker notion,the witness indistinguishable protocol,the proof of soundness can still go through.